Well, I've had some time for more of a play with this today, and found some clues in the "tag file info templates.xml" file...
So, currently, the expanded/collapsed state is not remembered, and I've figured out why the behaviour is confusing...
If you set the expanded/collapsed state of all the groups the way you would want them, then hit "Customise", make no no changes at all, and press OK.
Now, the states of each groups are set, and remembered each time the tag window is opened.
The confusion is arising because this is obviously happening when we quickly dive in to "Customise" to add a field to a group, with no thought at all as to what's expanded and what's collapsed, and when we hit "OK", the group states are updated and from that point forward that's how the tag window will open each time. We need to set them how we want them and dive into customise, and press OK to have the states saved.
We should be able to set the group state in the customise tool, always expanded or always collapsed, and that setting shouldn't change unless we specifically change it.
-marko